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Pure Mathematics

Pure Mathematics is a research area within which you can focus your studies as part of our suite of Mathematics research programmes (MPhil, PhD).

The following specialisations are available within this research area:

  • Ordinary and partial differential equations
  • Functional analysis
  • Analytical and computational spectral theory
  • Quantum mechanics
  • Number theory and its applications
  • Mathematical physics
  • Operator algebras and Noncommutative Geometry
  • Algebraic geometry
  • Algebraic topology
  • K-theory
  • Combinatorics
  • Quantum field theory and statistical mechanics
  • Conformal field theory and vertex operator algebras

Three research networks have been coordinated from Cardiff:

  • the EU-TMR Network on Non-Commutative Geometry
  • the EPSRC Network on Algebraic Geometry, Boundary Conformal Field Theory and Non- Commutative Geometry
  • the EPSRC Network on Spectral Theory (jointly with a group from the School of Computer Science).


Academic contact(s)

Professor Karl Schmidt

Professor Karl Schmidt


+44 (0)29 2087 6778

Pure Mathematics research is conducted within the Mathematical Analysis Research Group and the Geometry, Algebra, Mathematical Physics and Topology Research Group.  For information regarding these groups and their work, see their webpages:


You can search our studentships or find out more about funding.

Tuition fees

Students from the UK

Get the latest information on postgraduate fees.

Students from the EU, EEA and Switzerland

Get the latest information on postgraduate fees.

Students from the rest of the world (international)

Get the latest information on postgraduate fees.

Programme information

For programme structure, entry requirements and how to apply, visit the Mathematics programme.

View programme
See the range of PhD studentships and projects currently available.

Related courses

Related subjects